I attach a diagram which I drew of how the argument is unfolding (which is what I'm studying as a philosopher). Perhaps you'll have thoughts on how to improve it, or ideas of how to use the diagram.

I include the perspectives of 8 groups. I color coded:

General principles. (Black) These can't change because they are part of self-identity. Anti-Soviets are necessarily "anti soviet", for example.

Opinions and observations. (Blue) These can change but its not easy.

Decisions enacted. (Red) These are actions taken which are hard to undo. This is the common history that the different groups have to deal with. I also noted some events that are gamechangers, typically because they sideline one of the groups (like the fall of the Soviet Union).

Inspirations. (Green) These are ideas, strategies or outlooks that expand the possible solutions.

In this simple model, I have distinguished two broad groups of Lithuanians:

anti-Soviets (former "dissidents"), who speak of Soviet-occupied Lithuania, and for whom "Soviet culture should be completely undone".

post-Soviets (former "collaborators"), who speak of "Tarybų Lietuva", and for whom "We can be nostalgic for Soviet Lithuanian culture".

I attribute to the latter two inspirations which helped the Sports Palace get on the Cultural Heritage Registrar:

"Soviet Lithuanian creativity was anti-Soviet resistance"

"The Sports Palace was a historic site in Lithuania's quest for independence"

This seems to have kept the Sports Palace from being demolished and replaced with apartment buildings.

"The building is valuable, first of all, as the first in the Soviet Union built especially for sport and for spectators. Architecturally it is not so original, as is its cable-stayed structure, which was nowhere else. That has its own inner meaning, because that was our resistance through architectural expression. The palace was created as an object that would show up Moscow ("wipe its nose"). And truly - it won a USSR Council of Ministers award. And thereby it established, that our architectural culture is higher than theirs. This is the point and the value of this monument."

And he made a similar argument regarding the Soviet Lithuanian statues on the Green Bridge (which were recently removed, nevertheless):
http://www.ve.lt/naujienos/visuomene/sociumas/architektas-jonas-minkevicius-issigandome-patys-saves-1386947/
His point is that these statues are a "degradation" as regards artistic merit (the level was higher before the war) but they can be respected as "a compromise with one's conscience", "a struggle to survive or to perish", "to be or not to be". "It is a monument to history. The condition we were subject to. And also a monument to our invincibility, our inner hardiness."

My diagram suggests that for the Lithuanian government to change its position there needs to be support for the Jewish cemetery from both the anti-Soviet and post-Soviet perspectives. From the anti-Soviet side we can speak with the argument "What do wish to see from Gediminas castle, the Grand Duchy heritage (the Jewish cemetery), or the Soviet heritage (the Sports Palace)." The paradox is that the anti-Soviets also tend to be not-Jewish-minded and so instinctively prefer the Sports Palace until made conscious of the absurdity. Which is to say, it is a good argument to make.

However, there needs to be a separate argument for the post-Soviets. Here I suggest to build on Jonas Minkevičius line of thinking. Basically, Soviet Lithuanian culture is to be treasured not because it was objectively great (generally, it wasn't) but because it was indeed an "inner resistance" by distinguishing us from generic Soviet culture and the dominance of Moscow and its imperatives. So then Soviet Lithuanian culture should be honored with a respectful Museum of Soviet Lithuanian Culture where it could be presented in the proper context. And then we can say that the objectively "degenerate" artefacts can be removed from our public life. As a plus, the museum could incorporate the concrete and the furnishings that we'll have when we dismantle the Sports Palace.

I suppose that's the message of my talk. I'm curious what you think, or what else you think is perhaps more important, as regards winning over all sides.